Which method shows the two triangles are congruent
There are several methods to show that two triangles are congruent.
1. Side-Side-Side (SSS) Congruence: If all three sides of one triangle are equal to the corresponding three sides of another triangle, then the two triangles are congruent.
2. Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
3. Angle-Side-Angle (ASA) Congruence: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.
4. Angle-Angle-Side (AAS) Congruence: If two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
5. Hypotenuse-Leg (HL) Congruence: If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
Depending on the information given about the two triangles, we can use one of these methods to show that they are congruent.
To show that two triangles are congruent, you need to apply one of the congruence criteria. Here are several methods to demonstrate that two triangles are congruent:
1. Side-Side-Side (SSS) criterion: If the lengths of the corresponding sides of two triangles are equal, then the triangles are congruent.
2. Side-Angle-Side (SAS) criterion: If one side and the two adjacent angles of one triangle are equal to the corresponding side and angles of another triangle, then the triangles are congruent.
3. Angle-Side-Angle (ASA) criterion: If two angles and the included side of one triangle are equal to the corresponding angles and the included side of another triangle, then the triangles are congruent.
4. Angle-Angle-Side (AAS) criterion: If two angles and a non-included side of one triangle are equal to the corresponding angles and non-included side of another triangle, then the triangles are congruent.
5. Hypotenuse-Leg (HL) criterion (only for right triangles): If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
By using any of these congruence criteria, you can determine if two triangles are congruent.